The holy grail of digital advertising is tying an ad -- any ad running on any digital property -- to a subsequent product sale. Facebook, Google, AOL, Yahoo, Amazon, Twitter and other top digital ad sellers are pursuing it. But Facebook increasingly appears to be closest to success, according to industry executives following the quest.

Most recently, Facebook has run a small test with a brick-and-mortar retailer, tracing ads that ran in one of multiple third-party mobile apps to sales made in one of the retailer's stores. "We actually connected their point-of-sale [system] and were able to connect it through -- just like with one location with one little experiment," said David Jakubowski, Facebook's head of ad tech. "They were able to show there was a 13% lift in sales as a result of a whole bunch of this mobile activity."

Here's how Facebook is getting there. First, Facebook's registered user base of more than 1.4 billion people give it a way to track many people's online behavior whether they're on or off Facebook. Facebook can see when users are on certain third-party mobile apps and deliver an ad based on things you like on Facebook. Second, there's the company's Atlas ad server and the growing ad-tech business Facebook has built around it.

When Facebook bought Atlas from Microsoft in February 2013, "it took everyone by surprise because there were only a few people that thought Atlas still existed," said Andrew Casale, CEO of Index Exchange, an ad-tech firm that helps publishers automate their ad sales. Atlas was considered a dinosaur, and the meteor had already landed. Apple released the iPhone in 2007, and by 2013 people were migrating to mobile in droves. That's why Facebook had made such a big deal in 2012 about becoming a mobile-first company. Atlas's strength, however, was on the desktop.

"When I joined [Facebook in April 2014], the Atlas product that was in market was very similar to a lot of the technology that is still in market with some of the other ad servers," said Mr. Jakubowski. "It was very desktop-focused. It was all cookie-based. And it actually had a pretty high utility function going back five, ten years where the average consumer was interacting with digital assets primarily on the desktop in the WWW kind of world."

Atlas needed to adapt or die. "The engineering team [at Facebook] was really, really focused on solving that problem, building a parallel product right when I walked in," Mr. Jakubowski said.

Why acquire Atlas if only to rebuild it? Brian Boland, Facebook's VP of advertising technology, cited two reasons. It had a built-in customer base with clients like Atlas's former owner Microsoft, SolarCity, 1-800-Flowers and Coastal Contacts that knew Atlas's product and could chime in on its upgrade. And perhaps more importantly, Facebook wanted Atlas's team of engineers and executives well-versed in the kind of multi-touch attribution that Facebook believed was the foundation of the digital advertising's future.

Like every modern ad server, Atlas relied on cookies, little pieces of code that track users around the web but can't follow them from deskptop to mobile and back again. The more that people switch between their phones and tablets and laptops, the less valuable the cookie is -- unless there's a way to connect cookies.

"Moving away from a cookie-based solution is a critical part of improving accuracy, buying more efficiently, driving better performance and in general having better visibility into where your dollars are going as an advertiser," said Adam Kasper, Chief Media Officer at Havas Media North America.

Enter the Facebook user ID. If you're logged in to Facebook's site or mobile apps, then Facebook can ask publishers to put pieces of code in their sites or apps that tell Facebook, "Hey, user 12345 is here." That anonymized identification enables Facebook to connect user 12345 back to that person's Facebook account and whatever other information Facebook has on them. If a site's cookie is wrong about you, because you're using a shared computer for example, Facebook can correct the record.

"Within a mobile app environment where the cookie is no longer relevant, our people-based approach is very meaningful because you can start understanding the types of people that are in an app and their behavior as they travel between apps and from apps into the web," said Mark Trefgarne, who was the CEO of LiveRail, a video ad-tech firm that Facebook bought in 2014, and is now LiveRail's Product Management Director.

"What I think is really significant about their investment in Atlas is that they have a deterministic vision versus a probabilistic vision of what ad serving should be: a user ID or a device ID tethered to first-party cookies. It's absolutely significant and moving the industry quickly to not be distressed about the cookie going away but be excited. I credit Facebook for that," said 360i President Jared Belsky.

Facebook rolled out its rebuilt Atlas last September, pitching advertisers the ability to choose the ads they show someone based on the ads they had previously seen and the information Facebook had on that person. It also promised to measure the ads' performance across devices.

"The art of attribution is to infer whether the expected results happened," Mr. Casale said. "In the case of Facebook, it's not even a question. They can just confirm, which puts them in a pretty powerful position."

Ticket sales giant Live Nation, for example, used Atlas to promote Madonna's 2015 tour and was able to recognize that 66% of the tour's desktop sales followed ads run in mobile apps like dating app Grindr.

"Overall we see that 41% of those actions that are taken, those sales that are generated, start on one device and move to another device," Mr. Jakubowski said.

"Facebook has a huge advantage in the persistent log-in and human data, which none of the other ad servers really have at scale or have based on the nature of their technology or platform," Mr. Kasper said.

But Facebook has one inherent disadvantage compared to older ad servers. Getting an advertiser to switch ad servers is like getting someone to buy a new house. "It takes time for a solution like [Atlas] to take a major percentage of our business at both the agency and account level," said Mr. Kasper, whose agency Havas Media signed a deal with Facebook earlier this year to make Atlas available as an ad-serving option to clients.

Unlike a media buy or commissioning a content production, an ad server needs to be tested before an advertiser can commit to it. "Moving a client from one platform they've been on for 10 years to a new one is not a decision to be taken lightly. Proper evaluations and testing need to go into it," Mr. Kasper said. Beyond gauging an ad server's ability to identify and target the correct audiences, agencies like Havas Media need to check its performance with different ad formats, the ability to retrieve data from it for analytics, its ability to incorporate third-party data for ad targeting, the speed at which it can be adopted and the speed on which agencies' and advertisers' employees can be trained on using it and getting it up and running, according to Mr. Kasper. "It's done well in the tests we've done," he said.

(If anything, upgrading Atlas posed a bit of a risk for Facebook, because it meant effectively switching clients over to a new system -- making it an opportune time for clients to kick the tires on rival servers. Atlas wound up holding on to all its pre-existing customers.)

After migrating its original Atlas clients to the updated version, Facebook saw a 150% increase in impresions on the platform from March 2015 to June 2015, Mr. Boland said.

The revamped Atlas remains in the testing phase for many of the agencies using it so far. Omnicom was the first agency holding company to sign on, but Google's DoubleClick remains its primary ad server, said Omnicom Digital CEO Jonathan Nelson. "We have a deep, extensive relationship with Google," he said. "But a competitive landscape is good." The same goes for Havas Media, which has "a few [clients] active on it and a larger few who are strongly considering it," said Mr. Kasper.

"The people I trust in my product development and tech-ops team kicked the tires [on Atlas] and told me it is ready for primetime," said 360i's Mr. Belsky. "I know at the Denstu Aegis level, we have some pilots underway. You can't mess around with ad serving. It's not like I'm killing $10k off to try BuzzFeed. This is a pretty significant 'test.'"

Given the long-lead time it takes for an advertiser to switch ad servers, Facebook lets brands take Atlas for a test drive before committing to "completely" switch to the ad server, Mr. Boland said. That strategy appears to be working, if slowly.

It's not only advertisers Facebook is now looking to win over. Since Facebook introduced the revamped Atlas in fall 2014, "what we get overwhelmingly is we get apps and publishers coming to us saying 'How do I let Atlas measure me?' That's the thing I'm getting more than anything else when we're out in market," Mr. Jakubowski said. "How can I get measured because I have a good audience, but I'm not showing up fairly because my audience is on mobile?"

Publishers have become a newer area of focus for Facebook. The social network has already overtaken Google as the dominant digital ad seller in the U.S. based on share of display revenue, with eMarketer projecting Facebook to take 25% of the market this year compared to second-place Google's 13%. But the LiveRail acquisition and introduction of Facebook's mobile in-app ad network Audience Network has given it a foothold with other publishers.

Because LiveRail doesn't handle desktop display ads, however, Facebook can only do so much for publishers that aren't mobile-only, said Domenic Venuto, General Manager of The Weather Company's ad-tech division AdFX.

"Facebook's challenge is how to support the entire ecosystem," Mr. Venuto said. "People-based marketing and mobile platforms certainly are the future, but we all have existing businesses to support today. Their challenge is going to be how do they support publishers' existing businesses. There are many of us who have multiple platforms, and our advertisers like a cross-platform solution."

Add that to the list of things Facebook still needs to do to rival Google's, AOL's and Yahoo's ad-tech stacks. All of these companies are assembling one-stop ad-tech shops that can handle all the needs of advertisers and publishers. Facebook may later to the game than the others, but it's catching up quickly. "In any previous example of a big media company ad-teching up, we have never seen a rise this fast," Mr. Casale said.

In August 2014 tech news site The Information reported that Facebook was building a demand-side platform (DSP) that can be used to automatically place bids for advertisers in the real-time online auctions conducted by ad exchanges to sell off publishers' inventory. Mr. Jakubowski confirmed that development in a September 2014 interview with Ad Age, but Facebook has otherwise stayed quiet about that development. But Facebook's DSP doesn't appear to be only in development; it's live, to an extent.

Havas Media's Mr. Kasper confirmed that Facebook's DSP is currently being tested to buy ads outside of Facebook. "At this point the Atlas DSP cannot serve ads in Facebook, so that would be a useful capability," he siad. "I don't know the details as to why; I think the technologies didn't necessarily match up .... It's certainly part of their roadmap. It might even be this year. But the capability's not there from what I understand for them," he said. A Facebook spokeswoman declined to comment on any tests.

"We don't have anything new to talk about or announce on the DSP front other than that we're spending a lot of time with customers to figure out what they really need, how much of what we can do is helping them plan their campaigns versus execute their campaigns," Mr. Boland said. "That's important work that we're doing now as we build towards the next phase of product for Atlas."